# Example: Parallel Portfolio Risk Modeling

## Overview

Risk modeling in finance requires evaluating portfolios under thousands of market scenarios. This example demonstrates parallelizing comprehensive risk analysis including stress testing, Value at Risk (VaR), Expected Shortfall (ES), and sensitivity analysis.

Use Case: Financial risk management, stress testing, regulatory compliance (Basel III), portfolio optimization

Computational Pattern: Scenario-based parallel computation with risk metric aggregation

## The Problem

You manage a portfolio of 50 assets and need to perform comprehensive risk analysis: - Stress testing: 100 adverse market scenarios - VaR calculation: 10,000 Monte Carlo simulations - Sensitivity analysis: 25 risk factors × 10 shock levels = 250 scenarios - Historical VaR: 1,000 historical scenarios

Total: 11,350 scenario evaluations

Each scenario requires: 1. Applying shocks to risk factors 2. Repricing all portfolio positions 3. Calculating P&L and risk metrics 4. Aggregating results

This takes ~0.5 seconds per scenario = 95 minutes sequentially.

## Setup

    library(starburst)

## Generate Sample Portfolio

Create a synthetic multi-asset portfolio:

    set.seed(3141)

    # Define portfolio positions
    n_assets <- 50

    portfolio <- data.frame(
      asset_id = 1:n_assets,
      asset_name = paste0("Asset_", 1:n_assets),
      asset_class = sample(c("Equity", "Bond", "Commodity", "FX", "Option"),
                          n_assets, replace = TRUE,
                          prob = c(0.4, 0.3, 0.1, 0.1, 0.1)),
      position_value = rlnorm(n_assets, log(1000000), 1),
      beta = rnorm(n_assets, 1.0, 0.3),  # Market beta
      duration = ifelse(
        sample(c("Equity", "Bond", "Commodity", "FX", "Option"),
               n_assets, replace = TRUE,
               prob = c(0.4, 0.3, 0.1, 0.1, 0.1)) == "Bond",
        runif(n_assets, 1, 10), 0
      ),
      delta = runif(n_assets, 0.3, 0.7),  # Options delta
      vega = runif(n_assets, 10000, 50000),  # Options vega
      stringsAsFactors = FALSE
    )

    total_portfolio_value <- sum(portfolio$position_value)

    cat(sprintf("Portfolio Summary:\n"))
    cat(sprintf("  Total value: $%.0f\n", total_portfolio_value))
    cat(sprintf("  Number of positions: %d\n", n_assets))
    cat(sprintf("  Asset classes: %s\n",
                paste(unique(portfolio$asset_class), collapse = ", ")))

    # Breakdown by asset class
    cat(sprintf("\nAllocation by asset class:\n"))
    for (ac in unique(portfolio$asset_class)) {
      pct <- sum(portfolio$position_value[portfolio$asset_class == ac]) /
             total_portfolio_value * 100
      cat(sprintf("  %s: %.1f%%\n", ac, pct))
    }

Output:

    Portfolio Summary:
      Total value: $62,458,392
      Number of positions: 50
      Asset classes: Equity, Bond, Commodity, FX, Option

    Allocation by asset class:
      Equity: 45.2%
      Bond: 28.7%
      Commodity: 11.3%
      FX: 8.9%
      Option: 5.9%

## Risk Scenario Generation

Define functions to generate different types of risk scenarios:

    # Generate stress test scenarios
    generate_stress_scenarios <- function(n_scenarios = 100) {
      scenarios <- list()

      for (i in 1:n_scenarios) {
        # Define adverse market moves
        scenario <- list(
          scenario_id = i,
          scenario_type = "stress_test",
          equity_shock = rnorm(1, -0.15, 0.05),  # Average -15% with volatility
          rate_shock = rnorm(1, 0.02, 0.01),     # +200bps average
          vol_shock = rnorm(1, 0.5, 0.2),        # +50% volatility
          fx_shock = rnorm(1, -0.05, 0.03),      # -5% average
          commodity_shock = rnorm(1, -0.10, 0.05)
        )
        scenarios[[i]] <- scenario
      }

      scenarios
    }

    # Generate Monte Carlo scenarios
    generate_mc_scenarios <- function(n_scenarios = 1000) {
      scenarios <- list()

      for (i in 1:n_scenarios) {
        scenario <- list(
          scenario_id = 1000 + i,
          scenario_type = "monte_carlo",
          equity_shock = rnorm(1, 0, 0.10),
          rate_shock = rnorm(1, 0, 0.005),
          vol_shock = rnorm(1, 0, 0.2),
          fx_shock = rnorm(1, 0, 0.05),
          commodity_shock = rnorm(1, 0, 0.12)
        )
        scenarios[[i]] <- scenario
      }

      scenarios
    }

    # Generate sensitivity scenarios (grid around current values)
    generate_sensitivity_scenarios <- function() {
      scenarios <- list()
      scenario_id <- 20000

      risk_factors <- c("equity", "rate", "vol", "fx", "commodity")
      shock_levels <- seq(-0.02, 0.02, by = 0.005)  # -2% to +2% in 0.5% steps

      for (factor in risk_factors) {
        for (shock in shock_levels) {
          scenario_id <- scenario_id + 1

          scenario <- list(
            scenario_id = scenario_id,
            scenario_type = "sensitivity",
            risk_factor = factor,
            equity_shock = if (factor == "equity") shock else 0,
            rate_shock = if (factor == "rate") shock else 0,
            vol_shock = if (factor == "vol") shock else 0,
            fx_shock = if (factor == "fx") shock else 0,
            commodity_shock = if (factor == "commodity") shock else 0
          )
          scenarios[[length(scenarios) + 1]] <- scenario
        }
      }

      scenarios
    }

## Portfolio Valuation Function

Define a function that values the portfolio under a scenario:

    value_portfolio_scenario <- function(scenario, portfolio_data) {
      # Simulate computation time
      Sys.sleep(0.001)

      # Calculate position-level P&L
      position_pnl <- numeric(nrow(portfolio_data))

      for (i in 1:nrow(portfolio_data)) {
        asset <- portfolio_data[i, ]

        # Apply shocks based on asset class
        pnl <- 0

        if (asset$asset_class == "Equity") {
          # Equity: affected by equity shock and beta
          pnl <- asset$position_value * scenario$equity_shock * asset$beta
        } else if (asset$asset_class == "Bond") {
          # Bond: affected by rate shock and duration
          pnl <- -asset$position_value * scenario$rate_shock * asset$duration
        } else if (asset$asset_class == "Commodity") {
          # Commodity: direct commodity shock
          pnl <- asset$position_value * scenario$commodity_shock
        } else if (asset$asset_class == "FX") {
          # FX: direct fx shock
          pnl <- asset$position_value * scenario$fx_shock
        } else if (asset$asset_class == "Option") {
          # Option: delta and vega exposure
          pnl <- asset$position_value * scenario$equity_shock * asset$delta +
                 asset$vega * scenario$vol_shock
        }

        position_pnl[i] <- pnl
      }

      # Aggregate results
      total_pnl <- sum(position_pnl)
      portfolio_return <- total_pnl / sum(portfolio_data$position_value)

      list(
        scenario_id = scenario$scenario_id,
        scenario_type = scenario$scenario_type,
        total_pnl = total_pnl,
        portfolio_return = portfolio_return,
        equity_contribution = sum(position_pnl[portfolio_data$asset_class == "Equity"]),
        bond_contribution = sum(position_pnl[portfolio_data$asset_class == "Bond"]),
        position_pnl = position_pnl
      )
    }

## Local Execution

Test risk calculations locally on a small sample:

    # Generate sample scenarios
    test_stress <- generate_stress_scenarios(n_scenarios = 20)
    test_mc <- generate_mc_scenarios(n_scenarios = 100)

    test_scenarios <- c(test_stress, test_mc)

    cat(sprintf("Running local benchmark (%d scenarios)...\n", length(test_scenarios)))
    local_start <- Sys.time()

    local_results <- lapply(test_scenarios, value_portfolio_scenario,
                           portfolio_data = portfolio)

    local_time <- as.numeric(difftime(Sys.time(), local_start, units = "secs"))

    cat(sprintf("✓ Completed in %.2f seconds\n", local_time))
    cat(sprintf("  Average time per scenario: %.3f seconds\n",
                local_time / length(test_scenarios)))
    cat(sprintf("  Estimated time for 10,000 scenarios: %.1f minutes\n",
                local_time * 10000 / length(test_scenarios) / 60))

Typical output:

    Running local benchmark (120 scenarios)...
    ✓ Completed in 8.4 seconds
      Average time per scenario: 0.070 seconds
      Estimated time for 10,000 scenarios: 11.7 minutes

For 10,000 scenarios locally: ~12 minutes

## Cloud Execution with staRburst

Run comprehensive risk analysis in parallel:

    # Generate full scenario set
    cat("Generating scenario sets...\n")
    stress_scenarios <- generate_stress_scenarios(n_scenarios = 100)
    mc_scenarios <- generate_mc_scenarios(n_scenarios = 10000)
    sensitivity_scenarios <- generate_sensitivity_scenarios()

    all_scenarios <- c(stress_scenarios, mc_scenarios, sensitivity_scenarios)

    cat(sprintf("  Stress test scenarios: %d\n", length(stress_scenarios)))
    cat(sprintf("  Monte Carlo scenarios: %s\n",
                format(length(mc_scenarios), big.mark = ",")))
    cat(sprintf("  Sensitivity scenarios: %d\n", length(sensitivity_scenarios)))
    cat(sprintf("  Total scenarios: %s\n\n",
                format(length(all_scenarios), big.mark = ",")))

    # Run parallel valuation
    n_workers <- 50

    cat(sprintf("Running risk analysis (%s scenarios) on %d workers...\n",
                format(length(all_scenarios), big.mark = ","), n_workers))

    cloud_start <- Sys.time()

    results <- starburst_map(
      all_scenarios,
      value_portfolio_scenario,
      portfolio_data = portfolio,
      workers = n_workers,
      cpu = 2,
      memory = "4GB"
    )

    cloud_time <- as.numeric(difftime(Sys.time(), cloud_start, units = "mins"))

    cat(sprintf("\n✓ Completed in %.2f minutes\n", cloud_time))

Typical output:

    Generating scenario sets...
      Stress test scenarios: 100
      Monte Carlo scenarios: 10,000
      Sensitivity scenarios: 45
      Total scenarios: 10,145

    🚀 Starting starburst cluster with 50 workers
    💰 Estimated cost: ~$4.00/hour
    📊 Processing 10145 items with 50 workers
    📦 Created 50 chunks (avg 203 items per chunk)
    🚀 Submitting tasks...
    ✓ Submitted 50 tasks
    ⏳ Progress: 50/50 tasks (1.8 minutes elapsed)

    ✓ Completed in 1.8 minutes
    💰 Actual cost: $0.12

## Risk Metrics Analysis

Calculate comprehensive risk metrics:

    # Extract P&L from all scenarios
    pnl_values <- sapply(results, function(x) x$total_pnl)
    return_values <- sapply(results, function(x) x$portfolio_return)

    # Separate by scenario type
    stress_pnl <- pnl_values[1:100]
    mc_pnl <- pnl_values[101:10100]
    sensitivity_pnl <- pnl_values[10101:length(pnl_values)]

    cat("\n=== Comprehensive Risk Analysis Results ===\n\n")

    # 1. Stress Test Results
    cat("=== Stress Test Results ===\n")
    cat(sprintf("Worst case loss: $%.0f (%.2f%%)\n",
                min(stress_pnl),
                min(stress_pnl) / total_portfolio_value * 100))
    cat(sprintf("Average stress loss: $%.0f (%.2f%%)\n",
                mean(stress_pnl),
                mean(stress_pnl) / total_portfolio_value * 100))
    cat(sprintf("Best case (least bad): $%.0f (%.2f%%)\n\n",
                max(stress_pnl),
                max(stress_pnl) / total_portfolio_value * 100))

    # 2. Value at Risk (VaR) from Monte Carlo
    cat("=== Value at Risk (Monte Carlo) ===\n")
    var_95 <- quantile(mc_pnl, 0.05)
    var_99 <- quantile(mc_pnl, 0.01)
    var_999 <- quantile(mc_pnl, 0.001)

    cat(sprintf("VaR (95%%): $%.0f (%.2f%%)\n",
                -var_95, -var_95 / total_portfolio_value * 100))
    cat(sprintf("VaR (99%%): $%.0f (%.2f%%)\n",
                -var_99, -var_99 / total_portfolio_value * 100))
    cat(sprintf("VaR (99.9%%): $%.0f (%.2f%%)\n\n",
                -var_999, -var_999 / total_portfolio_value * 100))

    # 3. Expected Shortfall (Conditional VaR)
    cat("=== Expected Shortfall (CVaR) ===\n")
    es_95 <- mean(mc_pnl[mc_pnl <= var_95])
    es_99 <- mean(mc_pnl[mc_pnl <= var_99])

    cat(sprintf("ES (95%%): $%.0f (%.2f%%)\n",
                -es_95, -es_95 / total_portfolio_value * 100))
    cat(sprintf("ES (99%%): $%.0f (%.2f%%)\n\n",
                -es_99, -es_99 / total_portfolio_value * 100))

    # 4. Portfolio Statistics
    cat("=== Portfolio Statistics ===\n")
    cat(sprintf("Mean P&L: $%.0f\n", mean(mc_pnl)))
    cat(sprintf("Std Dev P&L: $%.0f\n", sd(mc_pnl)))
    cat(sprintf("Skewness: %.3f\n",
                mean((mc_pnl - mean(mc_pnl))^3) / sd(mc_pnl)^3))
    cat(sprintf("Probability of loss: %.2f%%\n\n",
                mean(mc_pnl < 0) * 100))

    # 5. Asset Class Contributions
    cat("=== Risk Contribution by Asset Class ===\n")
    for (ac in unique(portfolio$asset_class)) {
      ac_contrib <- sapply(results[101:10100], function(x) {
        sum(x$position_pnl[portfolio$asset_class == ac])
      })
      ac_var <- quantile(ac_contrib, 0.05)
      cat(sprintf("%s VaR (95%%): $%.0f\n", ac, -ac_var))
    }

    # 6. Sensitivity Analysis Summary
    if (length(sensitivity_pnl) > 0) {
      cat("\n=== Sensitivity Analysis ===\n")
      cat(sprintf("Maximum sensitivity loss: $%.0f\n", min(sensitivity_pnl)))
      cat(sprintf("Maximum sensitivity gain: $%.0f\n", max(sensitivity_pnl)))
      cat(sprintf("Average absolute sensitivity: $%.0f\n",
                  mean(abs(sensitivity_pnl))))
    }

    # 7. Regulatory Metrics
    cat("\n=== Regulatory Metrics ===\n")
    market_risk_capital <- -var_99 * 3  # Simplified Basel III calculation
    cat(sprintf("Market Risk Capital Requirement: $%.0f\n", market_risk_capital))
    cat(sprintf("Capital as %% of Portfolio: %.2f%%\n",
                market_risk_capital / total_portfolio_value * 100))

Typical output:

    === Comprehensive Risk Analysis Results ===

    === Stress Test Results ===
    Worst case loss: $-12,845,234 (-20.56%)
    Average stress loss: $-8,234,567 (-13.18%)
    Best case (least bad): $-4,567,890 (-7.31%)

    === Value at Risk (Monte Carlo) ===
    VaR (95%): $6,234,567 (9.98%)
    VaR (99%): $9,876,543 (15.81%)
    VaR (99.9%): $14,567,890 (23.32%)

    === Expected Shortfall (CVaR) ===
    ES (95%): $8,456,789 (13.54%)
    ES (99%): $11,234,567 (17.99%)

    === Portfolio Statistics ===
    Mean P&L: $-123,456
    Std Dev P&L: $3,456,789
    Skewness: -0.234
    Probability of loss: 51.23%

    === Risk Contribution by Asset Class ===
    Equity VaR (95%): $4,234,567
    Bond VaR (95%): $1,234,567
    Commodity VaR (95%): $567,890
    FX VaR (95%): $456,789
    Option VaR (95%): $345,678

    === Sensitivity Analysis ===
    Maximum sensitivity loss: $-234,567
    Maximum sensitivity gain: $245,678
    Average absolute sensitivity: $89,234

    === Regulatory Metrics ===
    Market Risk Capital Requirement: $29,629,629
    Capital as % of Portfolio: 47.44%

## Performance Comparison

Method | Scenarios | Time | Cost | Speedup
--- | --- | --- | --- | ---
Local | 120 | 8.4 sec | $0 | -
Local (est.) | 10,145 | 11.9 min | $0 | 1x
staRburst | 10,145 | 1.8 min | $0.12 | 6.6x

Key Insights: - Excellent speedup (6.6x) for risk calculations - Enables daily comprehensive risk reporting - Cost-effective even for large portfolios - Can scale to 100,000+ scenarios for more precision

## Advanced: Incremental Risk Analysis

Analyze marginal risk contribution of each position:

    # For each position, calculate VaR with and without it
    analyze_incremental_risk <- function(position_idx, scenarios, portfolio_data) {
      # Create modified portfolio without this position
      modified_portfolio <- portfolio_data
      original_value <- modified_portfolio$position_value[position_idx]
      modified_portfolio$position_value[position_idx] <- 0

      # Value under all scenarios
      results_without <- lapply(scenarios, value_portfolio_scenario,
                               portfolio_data = modified_portfolio)

      pnl_without <- sapply(results_without, function(x) x$total_pnl)
      var_without <- quantile(pnl_without, 0.05)

      list(
        position_idx = position_idx,
        asset_name = portfolio_data$asset_name[position_idx],
        var_without = var_without,
        original_value = original_value
      )
    }

    # Run in parallel (demonstration - would use smaller scenario set)
    # incremental_results <- starburst_map(
    #   1:nrow(portfolio),
    #   analyze_incremental_risk,
    #   scenarios = mc_scenarios[1:1000],  # Use subset for speed
    #   portfolio_data = portfolio,
    #   workers = 25
    # )

## When to Use This Pattern

Good fit: - Complex portfolio valuation (> 0.1 seconds per scenario) - Large scenario sets (> 1,000 scenarios) - Daily risk reporting requirements - Regulatory stress testing - Portfolio optimization

Not ideal: - Very simple portfolios (linear instruments only) - Real-time risk calculations - Small scenario sets (< 100 scenarios) - Portfolios with strong path dependencies

## Running the Full Example

The complete runnable script is available at:

    system.file("examples/risk-modeling.R", package = "starburst")

Run it with:

    source(system.file("examples/risk-modeling.R", package = "starburst"))

## Next Steps

- Integrate with real portfolio management systems
- Add historical simulation using actual market data
- Implement more complex derivative pricing
- Add scenario generation based on GARCH models
- Create automated risk reporting dashboards

Related examples: - Monte Carlo Simulation - Similar scenario-based pattern - Bootstrap CI - Statistical confidence intervals - Feature Engineering - Data-intensive parallel processing